Depending on the strop material if it comes apart, glue down any larger flaps /cuts then just sand the minor nicks with 2000 grit or higher paper,
then it can be softened with lather and a bottle
or use vitamin E type hand cream after rubbing your hands until not greasy,
or last resort neetsfoot oil or glicerine on realy dry leather,
if a cotton or linen back strop clean by soaking in Oxyaction or similar laundry powder then dry flat this could take a couple goes and then reassemble
Some old cottons like the illonoise strops have a white paste on them that can be cleaned the same way or left if ok
Got pics of the item would help
